Finite Group Databasebeta

← C73×#16270 #32925674

Subgroups — C73×#16270 #32925674

Order 18688.

2030 conjugacy classes of subgroups.

The subgroup lattice has 1302 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#397×C73C211yesmaximal, characteristic, complemented
2C2×#392×C73C211yesmaximal, characteristic
3C2×#386×C73C211yesmaximal, characteristic, complemented
4C2×#386×C73C211yesmaximal, characteristic, complemented
5C73×#1443C211yesmaximal, characteristic, complemented
6C73×#1443C211yesmaximal, characteristic, complemented
7C73×#1440C211yesmaximal, characteristic, complemented
8C73×#1440C211yesmaximal, characteristic, complemented
9C73×#1439C211yesmaximal, characteristic, complemented
10C73×#1439C211yesmaximal, characteristic, complemented
11C73×#1438C211yesmaximal, characteristic, complemented
12C73×#1438C211yesmaximal, characteristic, complemented
13C73×#1438C211yesmaximal, characteristic, complemented
14C73×#1438C211yesmaximal, characteristic, complemented
15C73×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C73C2211yescharacteristic
17C23×D4×C73C2211yescharacteristic
18C23×D4×C73C2211yescharacteristic
19C24×C4×C73C2211yescharacteristic
20C22×C4⋊C4×C73C2211yescharacteristic
21C22×C22⋊C4×C73C2211yescharacteristic
22C22×C22⋊C4×C73C2211yescharacteristic
23C22×C22⋊C4×C73C2211yescharacteristic
24C22×C22⋊C4×C73C2211yescharacteristic
25C22×C22⋊C4×C73C2211yescharacteristic
26C22×C22⋊C4×C73C2211yescharacteristic
27C22×C22⋊C4×C73C2211yescharacteristic
28C22×C22⋊C4×C73C2211yescharacteristic
29C22×C22⋊C4×C73C2211yescharacteristic
30C22×C22⋊C4×C73C2211yescharacteristic
31C22×C22⋊C4×C73C2211yescharacteristic
32C22×C22⋊C4×C73C2211yescharacteristic
33C22×C22⋊C4×C73C2211yescharacteristic
34C22×C22⋊C4×C73C2211yescharacteristic
35#397×C73—24no—
36#392×C73—24no—
37#386×C73—24no—
38#386×C73—24no—
39C2×#95×C73C2211yescharacteristic
40C2×#95×C73C2211yescharacteristic
41C2×#95×C73C2211yescharacteristic
42C2×#95×C73C2211yescharacteristic
43C2×#95×C73C2211yescharacteristic
44C2×#95×C73C2211yescharacteristic
45C2×#95×C73C2211yescharacteristic
46C2×#95×C73C2211yescharacteristic
47C2×#95×C73C2211yescharacteristic
48C2×#95×C73C2211yescharacteristic
49C2×#95×C73C2211yescharacteristic
50C2×#95×C73C2211yescharacteristic
51C2×#95×C73C2211yescharacteristic
52C2×#95×C73C2211yescharacteristic
53C2×#95×C73C2211yescharacteristic
54C2×#95×C73C2211yescharacteristic
55C25×C73C2311yescharacteristic
56C25×C73C2311yescharacteristic
57C25×C73C2311yescharacteristic
58C22×D4×C73—22no—
59C22×D4×C73—22no—
60C22×D4×C73—22no—
61C22×D4×C73—22no—
62C22×D4×C73—22no—
63C22×D4×C73—22no—
64C22×D4×C73—22no—
65C22×D4×C73—22no—
66C22×D4×C73—22no—
67C22×D4×C73—22no—
68C22×D4×C73—41no—
69C22×D4×C73—41no—
70C22×D4×C73—41no—
71C22×D4×C73—41no—
72C22×D4×C73—41no—
73C22×D4×C73—41no—
74C22×D4×C73—41no—
75C22×D4×C73—41no—
76C22×D4×C73—41no—
77C22×D4×C73—41no—
78C22×D4×C73D414yes—
79C23×C4×C73—22no—
80C23×C4×C73—22no—
81C23×C4×C73—22no—
82C23×C4×C73—41no—
83C23×C4×C73—41no—
84C23×C4×C73—41no—
85C23×C4×C73—41no—
86C23×C4×C73C2311yescharacteristic
87C23×C4×C73C2311yescharacteristic
88C23×C4×C73C2311yescharacteristic
89C23×C4×C73C2311yescharacteristic
90C23×C4×C73C2311yescharacteristic
91C23×C4×C73C2311yescharacteristic
92C23×C4×C73C2311yescharacteristic
93C23×C4×C73C2311yescharacteristic
94C23×C4×C73C2311yescharacteristic
95C23×C4×C73C2311yescharacteristic
96C23×C4×C73C2311yescharacteristic
97C23×C4×C73C2311yescharacteristic
98C2×C4⋊C4×C73—22no—
99C2×C4⋊C4×C73—41no—
100C2×C4⋊C4×C73—41no—
101C2×C22⋊C4×C73—22no—
102C2×C22⋊C4×C73—22no—
103C2×C22⋊C4×C73—22no—
104C2×C22⋊C4×C73—22no—
105C2×C22⋊C4×C73—22no—
106C2×C22⋊C4×C73—22no—
107C2×C22⋊C4×C73—22no—
108C2×C22⋊C4×C73—22no—
109C2×C22⋊C4×C73—22no—
110C2×C22⋊C4×C73—22no—
111C2×C22⋊C4×C73—22no—
112C2×C22⋊C4×C73—22no—
113C2×C22⋊C4×C73—22no—
114C2×C22⋊C4×C73—22no—
115C2×C22⋊C4×C73—22no—
116C2×C22⋊C4×C73—22no—
117C2×C22⋊C4×C73—22no—
118C2×C22⋊C4×C73—22no—
119C2×C22⋊C4×C73—41no—
120C2×C22⋊C4×C73—41no—
121C2×C22⋊C4×C73—41no—
122C2×C22⋊C4×C73—41no—
123C2×C22⋊C4×C73—41no—
124C2×C22⋊C4×C73—41no—
125C2×C22⋊C4×C73—41no—
126C2×C22⋊C4×C73—41no—
127C2×C22⋊C4×C73—41no—
128C2×C22⋊C4×C73—41no—
129C2×C22⋊C4×C73—41no—
130C2×C22⋊C4×C73—41no—
131C2×C22⋊C4×C73—41no—
132C2×C22⋊C4×C73—41no—
133C2×C22⋊C4×C73—41no—
134C2×C22⋊C4×C73—41no—
135C2×C22⋊C4×C73—41no—
136C2×C22⋊C4×C73—41no—
137C2×C22⋊C4×C73—41no—
138C2×C22⋊C4×C73—41no—
139C2×C22⋊C4×C73—41no—
140C2×C22⋊C4×C73—41no—
141C2×C22⋊C4×C73—41no—
142C2×C22⋊C4×C73—41no—
143#95×C73—22no—
144#95×C73—22no—
145#95×C73—22no—
146#95×C73—22no—
147#95×C73—22no—
148#95×C73—22no—
149#95×C73—22no—
150#95×C73—41no—
151#95×C73—41no—
152#95×C73—41no—
153#95×C73—41no—
154#95×C73—41no—
155#95×C73—41no—
156#95×C73—41no—
157#95×C73—41no—
158#95×C73D414yescomplemented
159C24×C73—21no—
160C24×C73—21no—
161C24×C73—21no—
162C24×C73—21no—
163C24×C73—21no—
164C24×C73—21no—
165C24×C73—21no—
166C24×C73—21no—
167C24×C73—21no—
168C24×C73—21no—
169C24×C73—21no—
170C24×C73—21no—
171C24×C73—21no—
172C24×C73—21no—
173C24×C73—21no—
174C24×C73—21no—
175C24×C73—21no—
176C24×C73—21no—
177C24×C73—21no—
178C24×C73—21no—
179C24×C73—21no—
180C24×C73—21no—
181C24×C73—21no—
182C24×C73—21no—
183C24×C73—21no—
184C24×C73—21no—
185C24×C73—21no—
186C24×C73—21no—
187C24×C73—21no—
188C24×C73—21no—
189C24×C73—21no—
190C24×C73—21no—
191C24×C73—21no—
192C24×C73—21no—
193C24×C73—21no—
194C24×C73—21no—
195C24×C73—21no—
196C24×C73—21no—
197C24×C73—21no—
198C24×C73—21no—
199C24×C73C2×D412yes—
200C24×C73C2×D412yes—
201C24×C73#4112yes—
202C24×C73#4112yes—
203C24×C73#4112yes—
204C24×C73C2411yescharacteristic
205C2×D4×C73—28no—
206C2×D4×C73—28no—
207C2×D4×C73—44no—
208C2×D4×C73—44no—
209C2×D4×C73—44no—
210C2×D4×C73—44no—
211C2×D4×C73—44no—
212C2×D4×C73—44no—
213C2×D4×C73—44no—
214C2×D4×C73—44no—
215C2×D4×C73—44no—
216C2×D4×C73—44no—
217C2×D4×C73—44no—
218C2×D4×C73—44no—
219C2×D4×C73—44no—
220C2×D4×C73—44no—
221C2×D4×C73—44no—
222C2×D4×C73—44no—
223C2×D4×C73—44no—
224C2×D4×C73—44no—
225C2×D4×C73—44no—
226C22×C4×C73—21no—
227C22×C4×C73—21no—
228C22×C4×C73—21no—
229C22×C4×C73—21no—
230C22×C4×C73—21no—
231C22×C4×C73—21no—
232C22×C4×C73—21no—
233C22×C4×C73—21no—
234C22×C4×C73—21no—
235C22×C4×C73—21no—
236C22×C4×C73—21no—
237C22×C4×C73—21no—
238C22×C4×C73—21no—
239C22×C4×C73—21no—
240C22×C4×C73—21no—
241C22×C4×C73—21no—
242C22×C4×C73—21no—
243C22×C4×C73—21no—
244C22×C4×C73—21no—
245C22×C4×C73—21no—
246C22×C4×C73—21no—
247C22×C4×C73—21no—
248C22×C4×C73—21no—
249C22×C4×C73—21no—
250C22×C4×C73—21no—
251C22×C4×C73—21no—
252C22×C4×C73—21no—
253C22×C4×C73—21no—
254C22×C4×C73—21no—
255C22×C4×C73—21no—
256C22×C4×C73—21no—
257C22×C4×C73—21no—
258C22×C4×C73—21no—
259C22×C4×C73—21no—
260C22×C4×C73—21no—
261C22×C4×C73—21no—
262C22×C4×C73—21no—
263C22×C4×C73—21no—
264C22×C4×C73—21no—
265C22×C4×C73—21no—
266C22×C4×C73—21no—
267C22×C4×C73—21no—
268C22×C4×C73—21no—
269C22×C4×C73—21no—
270C22×C4×C73—21no—
271C22×C4×C73—21no—
272C22×C4×C73—21no—
273C22×C4×C73—21no—
274C22×C4×C73—21no—
275C22×C4×C73—21no—
276C22×C4×C73—21no—
277C22×C4×C73—21no—
278C22×C4×C73—21no—
279C22×C4×C73—21no—
280C22×C4×C73—21no—
281C22×C4×C73—21no—
282C22×C4×C73—21no—
283C22×C4×C73—21no—
284C22×C4×C73—21no—
285C22×C4×C73—21no—
286C22×C4×C73—21no—
287C22×C4×C73—21no—
288C22×C4×C73—21no—
289C22×C4×C73—21no—
290C22×C4×C73—21no—
291C22×C4×C73—21no—
292C22×C4×C73—21no—
293C22×C4×C73—21no—
294C22×C4×C73—21no—
295C22×C4×C73—21no—
296C22×C4×C73—21no—
297C22×C4×C73—21no—
298C22×C4×C73—21no—
299C22×C4×C73—21no—
300C22×C4×C73—21no—
301C22×C4×C73—21no—
302C22×C4×C73—21no—
303C22×C4×C73—21no—
304C22×C4×C73—44no—
305C22×C4×C73—44no—
306C22×C4×C73—44no—
307C22×C4×C73—44no—
308C22×C4×C73—44no—
309C22×C4×C73—44no—
310C22×C4×C73—44no—
311C22×C4×C73C2×D412yes—
312C22×C4×C73C2×D412yes—
313C22×C4×C73C2×D412yes—
314C22×C4×C73C2×D412yes—
315C22×C4×C73#4112yes—
316C22×C4×C73#4112yes—
317C4⋊C4×C73—44no—
318C22⋊C4×C73—44no—
319C22⋊C4×C73—44no—
320C22⋊C4×C73—44no—
321C22⋊C4×C73—44no—
322C22⋊C4×C73—44no—
323C22⋊C4×C73—44no—
324C22⋊C4×C73—44no—
325C22⋊C4×C73—44no—
326C22⋊C4×C73—44no—
327C22⋊C4×C73—44no—
328C22⋊C4×C73—44no—
329C22⋊C4×C73—44no—
330C22⋊C4×C73—44no—
331C22⋊C4×C73—44no—
332C23×C73—22no—
333C23×C73—22no—
334C23×C73—22no—
335C23×C73—22no—
336C23×C73—22no—
337C23×C73—22no—
338C23×C73—22no—
339C23×C73—22no—
340C23×C73—22no—
341C23×C73—22no—
342C23×C73—22no—
343C23×C73—22no—
344C23×C73—22no—
345C23×C73—22no—
346C23×C73—22no—
347C23×C73—22no—
348C23×C73—22no—
349C23×C73—22no—
350C23×C73—22no—
351C23×C73—22no—
352C23×C73—22no—
353C23×C73—22no—
354C23×C73—22no—
355C23×C73—22no—
356C23×C73—22no—
357C23×C73—22no—
358C23×C73—22no—
359C23×C73—22no—
360C23×C73—22no—
361C23×C73—22no—
362C23×C73—22no—
363C23×C73—22no—
364C23×C73—41no—
365C23×C73—41no—
366C23×C73—41no—
367C23×C73—41no—
368C23×C73—41no—
369C23×C73—41no—
370C23×C73—41no—
371C23×C73—41no—
372C23×C73—41no—
373C23×C73—41no—
374C23×C73—41no—
375C23×C73—41no—
376C23×C73—41no—
377C23×C73—41no—
378C23×C73—41no—
379C23×C73—41no—
380C23×C73—41no—
381C23×C73—41no—
382C23×C73—41no—
383C23×C73—41no—
384C23×C73—41no—
385C23×C73—41no—
386C23×C73—41no—
387C23×C73—41no—
388C23×C73—41no—
389C23×C73—41no—
390C23×C73—41no—
391C23×C73—41no—
392C23×C73—41no—
393C23×C73—41no—
394C23×C73—41no—
395C23×C73—41no—
396C23×C73—41no—
397C23×C73—41no—
398C23×C73—41no—
399C23×C73—41no—
400C23×C73—41no—
401C23×C73—41no—
402C23×C73—41no—
403C23×C73—41no—
404C23×C73—41no—
405C23×C73—41no—
406C23×C73—41no—
407C23×C73—41no—
408C23×C73—41no—
409C23×C73—41no—
410C23×C73—41no—
411C23×C73—41no—
412C23×C73—41no—
413C23×C73—41no—
414C23×C73—41no—
415C23×C73—41no—
416C23×C73—41no—
417C23×C73—41no—
418C23×C73—41no—
419C23×C73—41no—
420C23×C73—41no—
421C23×C73—41no—
422C23×C73—41no—
423C23×C73—41no—
424C23×C73—41no—
425C23×C73—41no—
426C23×C73—41no—
427C23×C73—41no—
428C23×C73—41no—
429C23×C73—41no—
430C23×C73—41no—
431C23×C73—41no—
432C23×C73—41no—
433C23×C73—41no—
434C23×C73—41no—
435C23×C73—41no—
436C23×C73#12314yes—
437C23×C73C22×D411yescharacteristic
438C23×C73C22×D411yescharacteristic
439C23×C73C2×#4111yescharacteristic
440C23×C73C2×#4111yescharacteristic
441C23×C73C2×#4111yescharacteristic
442C23×C73C2×#4111yescharacteristic
443C23×C73C2×#4111yescharacteristic
444C23×C73H(5,𝔽2)11yescharacteristic
445C23×C73H(5,𝔽2)11yescharacteristic
446C23×C73H(5,𝔽2)11yescharacteristic
447C23×C73H(5,𝔽2)11yescharacteristic
448C23×C73H(5,𝔽2)11yescharacteristic
449C23×C73H(5,𝔽2)11yescharacteristic
450C23×C73H(5,𝔽2)11yescharacteristic
451C23×C73H(5,𝔽2)11yescharacteristic
452D4×C73—416no—
453D4×C73—416no—
454D4×C73—416no—
455C2×C4×C73—22no—
456C2×C4×C73—22no—
457C2×C4×C73—22no—
458C2×C4×C73—22no—
459C2×C4×C73—22no—
460C2×C4×C73—22no—
461C2×C4×C73—22no—
462C2×C4×C73—22no—
463C2×C4×C73—22no—
464C2×C4×C73—22no—
465C2×C4×C73—22no—
466C2×C4×C73—22no—
467C2×C4×C73—22no—
468C2×C4×C73—22no—
469C2×C4×C73—22no—
470C2×C4×C73—22no—
471C2×C4×C73—22no—
472C2×C4×C73—22no—
473C2×C4×C73—416no—
474C2×C4×C73—41no—
475C2×C4×C73—41no—
476C2×C4×C73—41no—
477C2×C4×C73—41no—
478C2×C4×C73—41no—
479C2×C4×C73—41no—
480C2×C4×C73—41no—
481C2×C4×C73—41no—
482C2×C4×C73—41no—
483C2×C4×C73—41no—
484C2×C4×C73—41no—
485C2×C4×C73—41no—
486C2×C4×C73—41no—
487C2×C4×C73—41no—
488C2×C4×C73—41no—
489C2×C4×C73—41no—
490C2×C4×C73—41no—
491C2×C4×C73—41no—
492C2×C4×C73—41no—
493C2×C4×C73—41no—
494C2×C4×C73—41no—
495C2×C4×C73—41no—
496C2×C4×C73—41no—
497C2×C4×C73—41no—
498C2×C4×C73—41no—
499C2×C4×C73—41no—
500C2×C4×C73—41no—
501C2×C4×C73—41no—
502C2×C4×C73—41no—
503C2×C4×C73—41no—
504C2×C4×C73—41no—
505C2×C4×C73—41no—
506C2×C4×C73—41no—
507C2×C4×C73—41no—
508C2×C4×C73—41no—
509C2×C4×C73—41no—
510C2×C4×C73—41no—
511C2×C4×C73—41no—
512C2×C4×C73—41no—
513C2×C4×C73—41no—
514C2×C4×C73—41no—
515C2×C4×C73—41no—
516C2×C4×C73—41no—
517C2×C4×C73—41no—
518C2×C4×C73—41no—
519C2×C4×C73—41no—
520C2×C4×C73—41no—
521C2×C4×C73—41no—
522C2×C4×C73—41no—
523C2×C4×C73—41no—
524C2×C4×C73—41no—
525C2×C4×C73—41no—
526C2×C4×C73—41no—
527C2×C4×C73—41no—
528C2×C4×C73—41no—
529C2×C4×C73—41no—
530C2×C4×C73—41no—
531C2×C4×C73—41no—
532C2×C4×C73—41no—
533C2×C4×C73—41no—
534C2×C4×C73—41no—
535C2×C4×C73—41no—
536C2×C4×C73—41no—
537C2×C4×C73—41no—
538C2×C4×C73—41no—
539C2×C4×C73—41no—
540C22×C73—24no—
541C22×C73—24no—
542C22×C73—24no—
543C22×C73—42no—
544C22×C73—42no—
545C22×C73—42no—
546C22×C73—42no—
547C22×C73—42no—
548C22×C73—42no—
549C22×C73—42no—
550C22×C73—42no—
551C22×C73—42no—
552C22×C73—42no—
553C22×C73—42no—
554C22×C73—42no—
555C22×C73—42no—
556C22×C73—42no—
557C22×C73—42no—
558C22×C73—42no—
559C22×C73—42no—
560C22×C73—42no—
561C22×C73—42no—
562C22×C73—42no—
563C22×C73—42no—
564C22×C73—42no—
565C22×C73—42no—
566C22×C73—42no—
567C22×C73—42no—
568C22×C73—42no—
569C22×C73—81no—
570C22×C73—81no—
571C22×C73—81no—
572C22×C73—81no—
573C22×C73—81no—
574C22×C73—81no—
575C22×C73—81no—
576C22×C73—81no—
577C22×C73—81no—
578C22×C73—81no—
579C22×C73—81no—
580C22×C73—81no—
581C22×C73—81no—
582C22×C73—81no—
583C22×C73—81no—
584C22×C73—81no—
585C22×C73C2×#12311yescharacteristic
586C22×C73#52511yescharacteristic
587C22×C73#52911yescharacteristic
588C22×C73#53411yescharacteristic
589C22×C73#53411yescharacteristic
590C22×C73#53511yescharacteristic
591C22×C73#53511yescharacteristic
592C22×C73#53811yescharacteristic
593C22×C73#53811yescharacteristic
594C22×C73#53811yescharacteristic
595C22×C73#53811yescharacteristic
596C22×C73#53811yescharacteristic
597C22×C73#53811yescharacteristic
598C22×C73#53811yescharacteristic
599C22×C73#53811yescharacteristic
600C22×C73#53811yescharacteristic
601C22×C73#53811yescharacteristic
602C22×C73#54011yescharacteristic
603C22×C73#54011yescharacteristic
604C22×C73D4211yescharacteristic
605C22×C73#54611yescharacteristic
606C22×C73#54611yescharacteristic
607C22×C73#54611yescharacteristic
608C22×C73#54611yescharacteristic
609C22×C73#54611yescharacteristic
610C22×C73#55011yescharacteristic
611C22×C73#55111yescharacteristic
612C22×C73#55111yescharacteristic
613C22×C73#55311yescharacteristic
614C22×C73#55311yescharacteristic
615C22×C73#55311yescharacteristic
616C22×C73#56011yescharacteristic
617C22×C73#56011yescharacteristic
618C22×C73#56011yescharacteristic
619C22×C73#56011yescharacteristic
620C4×C73—42no—
621C4×C73—42no—
622C4×C73—42no—
623C4×C73—42no—
624C4×C73—42no—
625C4×C73—42no—
626C4×C73—81no—
627C4×C73—81no—
628C4×C73—81no—
629C4×C73—81no—
630C4×C73—81no—
631C4×C73—81no—
632#16270C7311yesmaximal, characteristic, direct product factor, Sylow
633C2×C73—44no—
634C2×C73—82no—
635C2×C73—82no—
636C2×C73#241811yescharacteristic
637C2×C73#244411yescharacteristic
638C2×C73#246711yescharacteristic
639C2×C73#262211yescharacteristic
640C2×C73#263111yescharacteristic
641C2×C73#264811yescharacteristic
642C2×C73#267311yescharacteristic
643C2×C73#267811yescharacteristic
644C2×C73#268811yescharacteristic
645C2×C73#269711yescharacteristic
646C2×C73#270311yescharacteristic
647C2×C73#271411yescharacteristic
648C2×C73#274911yescharacteristic
649C2×C73#277811yescharacteristic
650C2×C73#282511yescharacteristic
651C2×#397C2×C7311yescharacteristic, complemented
652C2×#392C2×C7311yescharacteristic
653C2×#386C2×C7311yescharacteristic, complemented
654C2×#386C2×C7311yescharacteristic, complemented
655#1443C2×C7311yescharacteristic, complemented
656#1443C2×C7311yescharacteristic, complemented
657#1440C2×C7311yescharacteristic, complemented
658#1440C2×C7311yescharacteristic, complemented
659#1439C2×C7311yescharacteristic, complemented
660#1439C2×C7311yescharacteristic, complemented
661#1438C2×C7311yescharacteristic, complemented
662#1438C2×C7311yescharacteristic, complemented
663#1438C2×C7311yescharacteristic, complemented
664#1438C2×C7311yescharacteristic, complemented
665C22⋊#95C2×C7311yescharacteristic, complemented
666C73#1627011yescharacteristic, direct product factor, Sylow
667C23×D4C22×C7311yescharacteristic
668C23×D4C22×C7311yescharacteristic
669C23×D4C22×C7311yescharacteristic
670C24×C4C22×C7311yescharacteristic
671C22×C4⋊C4C22×C7311yescharacteristic
672C22×C22⋊C4C22×C7311yescharacteristic
673C22×C22⋊C4C22×C7311yescharacteristic
674C22×C22⋊C4C22×C7311yescharacteristic
675C22×C22⋊C4C22×C7311yescharacteristic
676C22×C22⋊C4C22×C7311yescharacteristic
677C22×C22⋊C4C22×C7311yescharacteristic
678C22×C22⋊C4C22×C7311yescharacteristic
679C22×C22⋊C4C22×C7311yescharacteristic
680C22×C22⋊C4C22×C7311yescharacteristic
681C22×C22⋊C4C22×C7311yescharacteristic
682C22×C22⋊C4C22×C7311yescharacteristic
683C22×C22⋊C4C22×C7311yescharacteristic
684C22×C22⋊C4C22×C7311yescharacteristic
685C22×C22⋊C4C22×C7311yescharacteristic
686#397—24no—
687#392—24no—
688#386—24no—
689#386—24no—
690C2×#95C22×C7311yescharacteristic
691C2×#95C22×C7311yescharacteristic
692C2×#95C22×C7311yescharacteristic
693C2×#95C22×C7311yescharacteristic
694C2×#95C22×C7311yescharacteristic
695C2×#95C22×C7311yescharacteristic
696C2×#95C22×C7311yescharacteristic
697C2×#95C22×C7311yescharacteristic
698C2×#95C22×C7311yescharacteristic
699C2×#95C22×C7311yescharacteristic
700C2×#95C22×C7311yescharacteristic
701C2×#95C22×C7311yescharacteristic
702C2×#95C22×C7311yescharacteristic
703C2×#95C22×C7311yescharacteristic
704C2×#95C22×C7311yescharacteristic
705C2×#95C22×C7311yescharacteristic
706C25C23×C7311yescharacteristic
707C25C23×C7311yescharacteristic
708C25C23×C7311yescharacteristic
709C22×D4—22no—
710C22×D4—22no—
711C22×D4—22no—
712C22×D4—22no—
713C22×D4—22no—
714C22×D4—22no—
715C22×D4—22no—
716C22×D4—22no—
717C22×D4—22no—
718C22×D4—22no—
719C22×D4—41no—
720C22×D4—41no—
721C22×D4—41no—
722C22×D4—41no—
723C22×D4—41no—
724C22×D4—41no—
725C22×D4—41no—
726C22×D4—41no—
727C22×D4—41no—
728C22×D4—41no—
729C22×D4D4×C7314yes—
730C23×C4—22no—
731C23×C4—22no—
732C23×C4—22no—
733C23×C4—41no—
734C23×C4—41no—
735C23×C4—41no—
736C23×C4—41no—
737C23×C4C23×C7311yescharacteristic
738C23×C4C23×C7311yescharacteristic
739C23×C4C23×C7311yescharacteristic
740C23×C4C23×C7311yescharacteristic
741C23×C4C23×C7311yescharacteristic
742C23×C4C23×C7311yescharacteristic
743C23×C4C23×C7311yescharacteristic
744C23×C4C23×C7311yescharacteristic
745C23×C4C23×C7311yescharacteristic
746C23×C4C23×C7311yescharacteristic
747C23×C4C23×C7311yescharacteristic
748C23×C4C23×C7311yescharacteristic
749C2×C4⋊C4—22no—
750C2×C4⋊C4—41no—
751C2×C4⋊C4—41no—
752C2×C22⋊C4—22no—
753C2×C22⋊C4—22no—
754C2×C22⋊C4—22no—
755C2×C22⋊C4—22no—
756C2×C22⋊C4—22no—
757C2×C22⋊C4—22no—
758C2×C22⋊C4—22no—
759C2×C22⋊C4—22no—
760C2×C22⋊C4—22no—
761C2×C22⋊C4—22no—
762C2×C22⋊C4—22no—
763C2×C22⋊C4—22no—
764C2×C22⋊C4—22no—
765C2×C22⋊C4—22no—
766C2×C22⋊C4—22no—
767C2×C22⋊C4—22no—
768C2×C22⋊C4—22no—
769C2×C22⋊C4—22no—
770C2×C22⋊C4—41no—
771C2×C22⋊C4—41no—
772C2×C22⋊C4—41no—
773C2×C22⋊C4—41no—
774C2×C22⋊C4—41no—
775C2×C22⋊C4—41no—
776C2×C22⋊C4—41no—
777C2×C22⋊C4—41no—
778C2×C22⋊C4—41no—
779C2×C22⋊C4—41no—
780C2×C22⋊C4—41no—
781C2×C22⋊C4—41no—
782C2×C22⋊C4—41no—
783C2×C22⋊C4—41no—
784C2×C22⋊C4—41no—
785C2×C22⋊C4—41no—
786C2×C22⋊C4—41no—
787C2×C22⋊C4—41no—
788C2×C22⋊C4—41no—
789C2×C22⋊C4—41no—
790C2×C22⋊C4—41no—
791C2×C22⋊C4—41no—
792C2×C22⋊C4—41no—
793C2×C22⋊C4—41no—
794#95—22no—
795#95—22no—
796#95—22no—
797#95—22no—
798#95—22no—
799#95—22no—
800#95—22no—
801#95—41no—
802#95—41no—
803#95—41no—
804#95—41no—
805#95—41no—
806#95—41no—
807#95—41no—
808#95—41no—
809#95D4×C7314yescomplemented
810C24—21no—
811C24—21no—
812C24—21no—
813C24—21no—
814C24—21no—
815C24—21no—
816C24—21no—
817C24—21no—
818C24—21no—
819C24—21no—
820C24—21no—
821C24—21no—
822C24—21no—
823C24—21no—
824C24—21no—
825C24—21no—
826C24—21no—
827C24—21no—
828C24—21no—
829C24—21no—
830C24—21no—
831C24—21no—
832C24—21no—
833C24—21no—
834C24—21no—
835C24—21no—
836C24—21no—
837C24—21no—
838C24—21no—
839C24—21no—
840C24—21no—
841C24—21no—
842C24—21no—
843C24—21no—
844C24—21no—
845C24—21no—
846C24—21no—
847C24—21no—
848C24—21no—
849C24—21no—
850C24C2×D4×C7312yes—
851C24C2×D4×C7312yes—
852C24#41×C7312yes—
853C24#41×C7312yes—
854C24#41×C7312yes—
855C24C24×C7311yescharacteristic
856C2×D4—28no—
857C2×D4—28no—
858C2×D4—44no—
859C2×D4—44no—
860C2×D4—44no—
861C2×D4—44no—
862C2×D4—44no—
863C2×D4—44no—
864C2×D4—44no—
865C2×D4—44no—
866C2×D4—44no—
867C2×D4—44no—
868C2×D4—44no—
869C2×D4—44no—
870C2×D4—44no—
871C2×D4—44no—
872C2×D4—44no—
873C2×D4—44no—
874C2×D4—44no—
875C2×D4—44no—
876C2×D4—44no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—44no—
956C22×C4—44no—
957C22×C4—44no—
958C22×C4—44no—
959C22×C4—44no—
960C22×C4—44no—
961C22×C4—44no—
962C22×C4C2×D4×C7312yes—
963C22×C4C2×D4×C7312yes—
964C22×C4C2×D4×C7312yes—
965C22×C4C2×D4×C7312yes—
966C22×C4#41×C7312yes—
967C22×C4#41×C7312yes—
968C4⋊C4—44no—
969C22⋊C4—44no—
970C22⋊C4—44no—
971C22⋊C4—44no—
972C22⋊C4—44no—
973C22⋊C4—44no—
974C22⋊C4—44no—
975C22⋊C4—44no—
976C22⋊C4—44no—
977C22⋊C4—44no—
978C22⋊C4—44no—
979C22⋊C4—44no—
980C22⋊C4—44no—
981C22⋊C4—44no—
982C22⋊C4—44no—
983C23—22no—
984C23—22no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—22no—
1012C23—22no—
1013C23—22no—
1014C23—22no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23#123×C7314yes—
1088C23C22×D4×C7311yescharacteristic
1089C23C22×D4×C7311yescharacteristic
1090C23C2×#41×C7311yescharacteristic
1091C23C2×#41×C7311yescharacteristic
1092C23C2×#41×C7311yescharacteristic
1093C23C2×#41×C7311yescharacteristic
1094C23C2×#41×C7311yescharacteristic
1095C23H(5,𝔽2)×C7311yescharacteristic
1096C23H(5,𝔽2)×C7311yescharacteristic
1097C23H(5,𝔽2)×C7311yescharacteristic
1098C23H(5,𝔽2)×C7311yescharacteristic
1099C23H(5,𝔽2)×C7311yescharacteristic
1100C23H(5,𝔽2)×C7311yescharacteristic
1101C23H(5,𝔽2)×C7311yescharacteristic
1102C23H(5,𝔽2)×C7311yescharacteristic
1103D4—416no—
1104D4—416no—
1105D4—416no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—416no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C22—24no—
1192C22—24no—
1193C22—24no—
1194C22—42no—
1195C22—42no—
1196C22—42no—
1197C22—42no—
1198C22—42no—
1199C22—42no—
1200C22—42no—
1201C22—42no—
1202C22—42no—
1203C22—42no—
1204C22—42no—
1205C22—42no—
1206C22—42no—
1207C22—42no—
1208C22—42no—
1209C22—42no—
1210C22—42no—
1211C22—42no—
1212C22—42no—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—42no—
1219C22—42no—
1220C22—81no—
1221C22—81no—
1222C22—81no—
1223C22—81no—
1224C22—81no—
1225C22—81no—
1226C22—81no—
1227C22—81no—
1228C22—81no—
1229C22—81no—
1230C22—81no—
1231C22—81no—
1232C22—81no—
1233C22—81no—
1234C22—81no—
1235C22—81no—
1236C22C2×#123×C7311yescharacteristic
1237C22#525×C7311yescharacteristic
1238C22#529×C7311yescharacteristic
1239C22#534×C7311yescharacteristic
1240C22#534×C7311yescharacteristic
1241C22#535×C7311yescharacteristic
1242C22#535×C7311yescharacteristic
1243C22#538×C7311yescharacteristic
1244C22#538×C7311yescharacteristic
1245C22#538×C7311yescharacteristic
1246C22#538×C7311yescharacteristic
1247C22#538×C7311yescharacteristic
1248C22#538×C7311yescharacteristic
1249C22#538×C7311yescharacteristic
1250C22#538×C7311yescharacteristic
1251C22#538×C7311yescharacteristic
1252C22#538×C7311yescharacteristic
1253C22#540×C7311yescharacteristic
1254C22#540×C7311yescharacteristic
1255C22D42×C7311yescharacteristic
1256C22#546×C7311yescharacteristic
1257C22#546×C7311yescharacteristic
1258C22#546×C7311yescharacteristic
1259C22#546×C7311yescharacteristic
1260C22#546×C7311yescharacteristic
1261C22#550×C7311yescharacteristic
1262C22#551×C7311yescharacteristic
1263C22#551×C7311yescharacteristic
1264C22#553×C7311yescharacteristic
1265C22#553×C7311yescharacteristic
1266C22#553×C7311yescharacteristic
1267C22#560×C7311yescharacteristic
1268C22#560×C7311yescharacteristic
1269C22#560×C7311yescharacteristic
1270C22#560×C7311yescharacteristic
1271C4—42no—
1272C4—42no—
1273C4—42no—
1274C4—42no—
1275C4—42no—
1276C4—42no—
1277C4—81no—
1278C4—81no—
1279C4—81no—
1280C4—81no—
1281C4—81no—
1282C4—81no—
1283C2—44no—
1284C2—82no—
1285C2—82no—
1286C2C73×#241811yescharacteristic
1287C2C73×#244411yescharacteristic
1288C2C73×#246711yescharacteristic
1289C2C73×#262211yescharacteristic
1290C2C73×#263111yescharacteristic
1291C2C73×#264811yescharacteristic
1292C2C73×#267311yescharacteristic
1293C2C73×#267811yescharacteristic
1294C2C73×#268811yescharacteristic
1295C2C73×#269711yescharacteristic
1296C2C73×#270311yescharacteristic
1297C2C73×#271411yescharacteristic
1298C2C73×#274911yescharacteristic
1299C2C73×#277811yescharacteristic
1300C2C73×#282511yescharacteristic
subgroupG/H
center, socleC24×C73C24
commutator, Frattini, cosocleC24C24×C73
prime radicalC2×#392×C73C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C73 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#397×C73C2semidirect
3. C2×#386×C73C2semidirect
4. C2×#386×C73C2semidirect
5. C73×#1443C2semidirect
6. C73×#1443C2semidirect
7. C73×#1440C2semidirect
8. C73×#1440C2semidirect
9. C73×#1439C2semidirect
10. C73×#1439C2semidirect
11. C73×#1438C2semidirect
12. C73×#1438C2semidirect
13. C73×#1438C2semidirect
14. C73×#1438C2semidirect
15. C73×C22⋊#95C2semidirect
158. #95×C73D4semidirect
632. #16270C73direct (N × H)
651. C2×#397C2×C73semidirect
653. C2×#386C2×C73semidirect
654. C2×#386C2×C73semidirect
655. #1443C2×C73semidirect
656. #1443C2×C73semidirect
657. #1440C2×C73semidirect
658. #1440C2×C73semidirect
659. #1439C2×C73semidirect
660. #1439C2×C73semidirect
661. #1438C2×C73semidirect
662. #1438C2×C73semidirect
663. #1438C2×C73semidirect
664. #1438C2×C73semidirect
665. C22⋊#95C2×C73semidirect
666. C73#16270direct (N × H)
809. #95D4×C73semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#397×C732
C2×#392×C732
C2×#386×C732
C73×#14432
C73×#14402
C73×#14392
C73×#14382
C73×C22⋊#952
#1627073